LMFDB - Embedded newform 8035.2.a.e.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41769 q^{2} -0.844619 q^{3} +3.84521 q^{4} +1.00000 q^{5} +2.04202 q^{6} +0.104455 q^{7} -4.46113 q^{8} -2.28662 q^{9} +O(q^{10})$	\(q-2.41769 q^{2} -0.844619 q^{3} +3.84521 q^{4} +1.00000 q^{5} +2.04202 q^{6} +0.104455 q^{7} -4.46113 q^{8} -2.28662 q^{9} -2.41769 q^{10} -4.33837 q^{11} -3.24773 q^{12} +1.66281 q^{13} -0.252539 q^{14} -0.844619 q^{15} +3.09520 q^{16} -2.04843 q^{17} +5.52833 q^{18} -3.17857 q^{19} +3.84521 q^{20} -0.0882245 q^{21} +10.4888 q^{22} -3.39580 q^{23} +3.76795 q^{24} +1.00000 q^{25} -4.02016 q^{26} +4.46518 q^{27} +0.401650 q^{28} +3.48617 q^{29} +2.04202 q^{30} +1.88643 q^{31} +1.43905 q^{32} +3.66427 q^{33} +4.95246 q^{34} +0.104455 q^{35} -8.79252 q^{36} -2.54978 q^{37} +7.68478 q^{38} -1.40444 q^{39} -4.46113 q^{40} +1.81376 q^{41} +0.213299 q^{42} -6.32258 q^{43} -16.6819 q^{44} -2.28662 q^{45} +8.20998 q^{46} +10.7097 q^{47} -2.61426 q^{48} -6.98909 q^{49} -2.41769 q^{50} +1.73014 q^{51} +6.39386 q^{52} -11.1272 q^{53} -10.7954 q^{54} -4.33837 q^{55} -0.465986 q^{56} +2.68468 q^{57} -8.42845 q^{58} +13.0910 q^{59} -3.24773 q^{60} -8.38124 q^{61} -4.56079 q^{62} -0.238848 q^{63} -9.66955 q^{64} +1.66281 q^{65} -8.85906 q^{66} -13.6304 q^{67} -7.87663 q^{68} +2.86816 q^{69} -0.252539 q^{70} -0.521308 q^{71} +10.2009 q^{72} -4.01401 q^{73} +6.16457 q^{74} -0.844619 q^{75} -12.2223 q^{76} -0.453164 q^{77} +3.39551 q^{78} +12.4879 q^{79} +3.09520 q^{80} +3.08848 q^{81} -4.38511 q^{82} -2.23895 q^{83} -0.339241 q^{84} -2.04843 q^{85} +15.2860 q^{86} -2.94448 q^{87} +19.3540 q^{88} -15.5780 q^{89} +5.52833 q^{90} +0.173689 q^{91} -13.0575 q^{92} -1.59331 q^{93} -25.8927 q^{94} -3.17857 q^{95} -1.21545 q^{96} -16.2681 q^{97} +16.8974 q^{98} +9.92020 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) $ 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.41769	−1.70956	−0.854781	−	0.518989i	$-0.826309\pi$
$2$	−2.41769	−1.70956	−0.854781	+	0.518989i	$0.826309\pi$
$3$	−0.844619	−0.487641	−0.243821	−	0.969820i	$-0.578401\pi$
$3$	−0.844619	−0.487641	−0.243821	+	0.969820i	$0.578401\pi$
$4$	3.84521	1.92260
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.04202	0.833653
$7$	0.104455	0.0394802	0.0197401	−	0.999805i	$-0.493716\pi$
$7$	0.104455	0.0394802	0.0197401	+	0.999805i	$0.493716\pi$
$8$	−4.46113	−1.57725
$9$	−2.28662	−0.762206
$10$	−2.41769	−0.764539
$11$	−4.33837	−1.30807	−0.654034	−	0.756465i	$-0.726925\pi$
$11$	−4.33837	−1.30807	−0.654034	+	0.756465i	$0.726925\pi$
$12$	−3.24773	−0.937540
$13$	1.66281	0.461182	0.230591	−	0.973051i	$-0.425934\pi$
$13$	1.66281	0.461182	0.230591	+	0.973051i	$0.425934\pi$
$14$	−0.252539	−0.0674938
$15$	−0.844619	−0.218080
$16$	3.09520	0.773799
$17$	−2.04843	−0.496817	−0.248409	−	0.968655i	$-0.579908\pi$
$17$	−2.04843	−0.496817	−0.248409	+	0.968655i	$0.579908\pi$
$18$	5.52833	1.30304
$19$	−3.17857	−0.729214	−0.364607	−	0.931162i	$-0.618797\pi$
$19$	−3.17857	−0.729214	−0.364607	+	0.931162i	$0.618797\pi$
$20$	3.84521	0.859814
$21$	−0.0882245	−0.0192522
$22$	10.4888	2.23622
$23$	−3.39580	−0.708073	−0.354037	−	0.935232i	$-0.615191\pi$
$23$	−3.39580	−0.708073	−0.354037	+	0.935232i	$0.615191\pi$
$24$	3.76795	0.769130
$25$	1.00000	0.200000
$26$	−4.02016	−0.788419
$27$	4.46518	0.859324
$28$	0.401650	0.0759047
$29$	3.48617	0.647365	0.323682	−	0.946166i	$-0.395079\pi$
$29$	3.48617	0.647365	0.323682	+	0.946166i	$0.395079\pi$
$30$	2.04202	0.372821
$31$	1.88643	0.338812	0.169406	−	0.985546i	$-0.445815\pi$
$31$	1.88643	0.338812	0.169406	+	0.985546i	$0.445815\pi$
$32$	1.43905	0.254390
$33$	3.66427	0.637868
$34$	4.95246	0.849340
$35$	0.104455	0.0176561
$36$	−8.79252	−1.46542
$37$	−2.54978	−0.419182	−0.209591	−	0.977789i	$-0.567213\pi$
$37$	−2.54978	−0.419182	−0.209591	+	0.977789i	$0.567213\pi$
$38$	7.68478	1.24664
$39$	−1.40444	−0.224891
$40$	−4.46113	−0.705366
$41$	1.81376	0.283262	0.141631	−	0.989920i	$-0.454765\pi$
$41$	1.81376	0.283262	0.141631	+	0.989920i	$0.454765\pi$
$42$	0.213299	0.0329128
$43$	−6.32258	−0.964184	−0.482092	−	0.876121i	$-0.660123\pi$
$43$	−6.32258	−0.964184	−0.482092	+	0.876121i	$0.660123\pi$
$44$	−16.6819	−2.51490
$45$	−2.28662	−0.340869
$46$	8.20998	1.21050
$47$	10.7097	1.56217	0.781085	−	0.624425i	$-0.214666\pi$
$47$	10.7097	1.56217	0.781085	+	0.624425i	$0.214666\pi$
$48$	−2.61426	−0.377336
$49$	−6.98909	−0.998441
$50$	−2.41769	−0.341912
$51$	1.73014	0.242268
$52$	6.39386	0.886669
$53$	−11.1272	−1.52844	−0.764220	−	0.644956i	$-0.776876\pi$
$53$	−11.1272	−1.52844	−0.764220	+	0.644956i	$0.776876\pi$
$54$	−10.7954	−1.46907
$55$	−4.33837	−0.584986
$56$	−0.465986	−0.0622700
$57$	2.68468	0.355595
$58$	−8.42845	−1.10671
$59$	13.0910	1.70430	0.852149	−	0.523299i	$-0.175299\pi$
$59$	13.0910	1.70430	0.852149	+	0.523299i	$0.175299\pi$
$60$	−3.24773	−0.419281
$61$	−8.38124	−1.07311	−0.536554	−	0.843866i	$-0.680274\pi$
$61$	−8.38124	−1.07311	−0.536554	+	0.843866i	$0.680274\pi$
$62$	−4.56079	−0.579220
$63$	−0.238848	−0.0300920
$64$	−9.66955	−1.20869
$65$	1.66281	0.206247
$66$	−8.85906	−1.09047
$67$	−13.6304	−1.66522	−0.832609	−	0.553861i	$-0.813154\pi$
$67$	−13.6304	−1.66522	−0.832609	+	0.553861i	$0.813154\pi$
$68$	−7.87663	−0.955182
$69$	2.86816	0.345286
$70$	−0.252539	−0.0301842
$71$	−0.521308	−0.0618678	−0.0309339	−	0.999521i	$-0.509848\pi$
$71$	−0.521308	−0.0618678	−0.0309339	+	0.999521i	$0.509848\pi$
$72$	10.2009	1.20219
$73$	−4.01401	−0.469805	−0.234902	−	0.972019i	$-0.575477\pi$
$73$	−4.01401	−0.469805	−0.234902	+	0.972019i	$0.575477\pi$
$74$	6.16457	0.716617
$75$	−0.844619	−0.0975282
$76$	−12.2223	−1.40199
$77$	−0.453164	−0.0516428
$78$	3.39551	0.384465
$79$	12.4879	1.40499	0.702497	−	0.711687i	$-0.252068\pi$
$79$	12.4879	1.40499	0.702497	+	0.711687i	$0.252068\pi$
$80$	3.09520	0.346053
$81$	3.08848	0.343164
$82$	−4.38511	−0.484254
$83$	−2.23895	−0.245756	−0.122878	−	0.992422i	$-0.539212\pi$
$83$	−2.23895	−0.245756	−0.122878	+	0.992422i	$0.539212\pi$
$84$	−0.339241	−0.0370143
$85$	−2.04843	−0.222183
$86$	15.2860	1.64833
$87$	−2.94448	−0.315682
$88$	19.3540	2.06315
$89$	−15.5780	−1.65127	−0.825634	−	0.564206i	$-0.809182\pi$
$89$	−15.5780	−1.65127	−0.825634	+	0.564206i	$0.809182\pi$
$90$	5.52833	0.582737
$91$	0.173689	0.0182075
$92$	−13.0575	−1.36134
$93$	−1.59331	−0.165219
$94$	−25.8927	−2.67063
$95$	−3.17857	−0.326114
$96$	−1.21545	−0.124051
$97$	−16.2681	−1.65178	−0.825889	−	0.563832i	$-0.809326\pi$
$97$	−16.2681	−1.65178	−0.825889	+	0.563832i	$0.809326\pi$
$98$	16.8974	1.70690
$99$	9.92020	0.997018
$100$	3.84521	0.384521
$101$	−7.87060	−0.783154	−0.391577	−	0.920145i	$-0.628070\pi$
$101$	−7.87060	−0.783154	−0.391577	+	0.920145i	$0.628070\pi$
$102$	−4.18294	−0.414173
$103$	−10.2337	−1.00836	−0.504180	−	0.863599i	$-0.668205\pi$
$103$	−10.2337	−1.00836	−0.504180	+	0.863599i	$0.668205\pi$
$104$	−7.41803	−0.727397
$105$	−0.0882245	−0.00860983
$106$	26.9021	2.61296
$107$	1.53276	0.148178	0.0740889	−	0.997252i	$-0.476395\pi$
$107$	1.53276	0.148178	0.0740889	+	0.997252i	$0.476395\pi$
$108$	17.1695	1.65214
$109$	13.3391	1.27765	0.638825	−	0.769352i	$-0.279421\pi$
$109$	13.3391	1.27765	0.638825	+	0.769352i	$0.279421\pi$
$110$	10.4888	1.00007
$111$	2.15359	0.204410
$112$	0.323308	0.0305497
$113$	13.0921	1.23160	0.615800	−	0.787902i	$-0.288833\pi$
$113$	13.0921	1.23160	0.615800	+	0.787902i	$0.288833\pi$
$114$	−6.49071	−0.607911
$115$	−3.39580	−0.316660
$116$	13.4050	1.24463
$117$	−3.80222	−0.351515
$118$	−31.6498	−2.91360
$119$	−0.213968	−0.0196144
$120$	3.76795	0.343966
$121$	7.82147	0.711043
$122$	20.2632	1.83455
$123$	−1.53194	−0.138130
$124$	7.25370	0.651401
$125$	1.00000	0.0894427
$126$	0.577460	0.0514442
$127$	−19.9805	−1.77298	−0.886491	−	0.462746i	$-0.846864\pi$
$127$	−19.9805	−1.77298	−0.886491	+	0.462746i	$0.846864\pi$
$128$	20.4998	1.81195
$129$	5.34017	0.470176
$130$	−4.02016	−0.352592
$131$	16.4794	1.43981	0.719905	−	0.694072i	$-0.244185\pi$
$131$	16.4794	1.43981	0.719905	+	0.694072i	$0.244185\pi$
$132$	14.0899	1.22637
$133$	−0.332017	−0.0287895
$134$	32.9540	2.84679
$135$	4.46518	0.384301
$136$	9.13831	0.783603
$137$	12.5847	1.07518	0.537590	−	0.843206i	$-0.319335\pi$
$137$	12.5847	1.07518	0.537590	+	0.843206i	$0.319335\pi$
$138$	−6.93430	−0.590287
$139$	−14.8147	−1.25657	−0.628283	−	0.777985i	$-0.716242\pi$
$139$	−14.8147	−1.25657	−0.628283	+	0.777985i	$0.716242\pi$
$140$	0.401650	0.0339456
$141$	−9.04562	−0.761778
$142$	1.26036	0.105767
$143$	−7.21391	−0.603257
$144$	−7.07753	−0.589794
$145$	3.48617	0.289510
$146$	9.70462	0.803160
$147$	5.90312	0.486881
$148$	−9.80444	−0.805920
$149$	11.6967	0.958230	0.479115	−	0.877752i	$-0.340958\pi$
$149$	11.6967	0.958230	0.479115	+	0.877752i	$0.340958\pi$
$150$	2.04202	0.166731
$151$	−3.33737	−0.271591	−0.135796	−	0.990737i	$-0.543359\pi$
$151$	−3.33737	−0.271591	−0.135796	+	0.990737i	$0.543359\pi$
$152$	14.1800	1.15015
$153$	4.68398	0.378677
$154$	1.09561	0.0882866
$155$	1.88643	0.151521
$156$	−5.40038	−0.432376
$157$	−3.39499	−0.270950	−0.135475	−	0.990781i	$-0.543256\pi$
$157$	−3.39499	−0.270950	−0.135475	+	0.990781i	$0.543256\pi$
$158$	−30.1917	−2.40193
$159$	9.39825	0.745330
$160$	1.43905	0.113767
$161$	−0.354707	−0.0279549
$162$	−7.46697	−0.586661
$163$	4.41601	0.345889	0.172944	−	0.984932i	$-0.444672\pi$
$163$	4.41601	0.345889	0.172944	+	0.984932i	$0.444672\pi$
$164$	6.97429	0.544600
$165$	3.66427	0.285263
$166$	5.41307	0.420136
$167$	−11.7157	−0.906589	−0.453295	−	0.891361i	$-0.649751\pi$
$167$	−11.7157	−0.906589	−0.453295	+	0.891361i	$0.649751\pi$
$168$	0.393581	0.0303654
$169$	−10.2350	−0.787312
$170$	4.95246	0.379836
$171$	7.26817	0.555811
$172$	−24.3116	−1.85374
$173$	−10.4578	−0.795095	−0.397548	−	0.917582i	$-0.630139\pi$
$173$	−10.4578	−0.795095	−0.397548	+	0.917582i	$0.630139\pi$
$174$	7.11883	0.539677
$175$	0.104455	0.00789604
$176$	−13.4281	−1.01218
$177$	−11.0569	−0.831086
$178$	37.6628	2.82295
$179$	5.05332	0.377703	0.188851	−	0.982006i	$-0.439524\pi$
$179$	5.05332	0.377703	0.188851	+	0.982006i	$0.439524\pi$
$180$	−8.79252	−0.655356
$181$	12.0260	0.893885	0.446942	−	0.894563i	$-0.352513\pi$
$181$	12.0260	0.893885	0.446942	+	0.894563i	$0.352513\pi$
$182$	−0.419925	−0.0311269
$183$	7.07896	0.523292
$184$	15.1491	1.11681
$185$	−2.54978	−0.187464
$186$	3.85213	0.282452
$187$	8.88685	0.649871
$188$	41.1810	3.00343
$189$	0.466409	0.0339263
$190$	7.68478	0.557513
$191$	10.2222	0.739653	0.369826	−	0.929101i	$-0.379417\pi$
$191$	10.2222	0.739653	0.369826	+	0.929101i	$0.379417\pi$
$192$	8.16709	0.589409
$193$	3.92688	0.282663	0.141332	−	0.989962i	$-0.454862\pi$
$193$	3.92688	0.282663	0.141332	+	0.989962i	$0.454862\pi$
$194$	39.3312	2.82382
$195$	−1.40444	−0.100574
$196$	−26.8745	−1.91961
$197$	−0.838466	−0.0597382	−0.0298691	−	0.999554i	$-0.509509\pi$
$197$	−0.838466	−0.0597382	−0.0298691	+	0.999554i	$0.509509\pi$
$198$	−23.9839	−1.70446
$199$	22.2877	1.57993	0.789966	−	0.613151i	$-0.210098\pi$
$199$	22.2877	1.57993	0.789966	+	0.613151i	$0.210098\pi$
$200$	−4.46113	−0.315449
$201$	11.5125	0.812029
$202$	19.0286	1.33885
$203$	0.364147	0.0255581
$204$	6.65276	0.465786
$205$	1.81376	0.126679
$206$	24.7420	1.72385
$207$	7.76490	0.539698
$208$	5.14673	0.356862
$209$	13.7898	0.953861
$210$	0.213299	0.0147190
$211$	−15.3686	−1.05802	−0.529009	−	0.848616i	$-0.677436\pi$
$211$	−15.3686	−1.05802	−0.529009	+	0.848616i	$0.677436\pi$
$212$	−42.7864	−2.93858
$213$	0.440306	0.0301693
$214$	−3.70574	−0.253319
$215$	−6.32258	−0.431196
$216$	−19.9197	−1.35537
$217$	0.197046	0.0133764
$218$	−32.2497	−2.18422
$219$	3.39031	0.229096
$220$	−16.6819	−1.12470
$221$	−3.40616	−0.229123
$222$	−5.20672	−0.349452
$223$	−0.113837	−0.00762312	−0.00381156	−	0.999993i	$-0.501213\pi$
$223$	−0.113837	−0.00762312	−0.00381156	+	0.999993i	$0.501213\pi$
$224$	0.150315	0.0100434
$225$	−2.28662	−0.152441
$226$	−31.6526	−2.10550
$227$	−13.7564	−0.913042	−0.456521	−	0.889713i	$-0.650905\pi$
$227$	−13.7564	−0.913042	−0.456521	+	0.889713i	$0.650905\pi$
$228$	10.3231	0.683667
$229$	26.0780	1.72328	0.861640	−	0.507520i	$-0.169438\pi$
$229$	26.0780	1.72328	0.861640	+	0.507520i	$0.169438\pi$
$230$	8.20998	0.541350
$231$	0.382751	0.0251831
$232$	−15.5522	−1.02105
$233$	22.1695	1.45237	0.726186	−	0.687499i	$-0.241291\pi$
$233$	22.1695	1.45237	0.726186	+	0.687499i	$0.241291\pi$
$234$	9.19258	0.600938
$235$	10.7097	0.698624
$236$	50.3375	3.27669
$237$	−10.5475	−0.685133
$238$	0.517308	0.0335321
$239$	−19.3646	−1.25259	−0.626296	−	0.779586i	$-0.715430\pi$
$239$	−19.3646	−1.25259	−0.626296	+	0.779586i	$0.715430\pi$
$240$	−2.61426	−0.168750
$241$	−4.97732	−0.320617	−0.160309	−	0.987067i	$-0.551249\pi$
$241$	−4.97732	−0.320617	−0.160309	+	0.987067i	$0.551249\pi$
$242$	−18.9099	−1.21557
$243$	−16.0041	−1.02667
$244$	−32.2276	−2.06316
$245$	−6.98909	−0.446517
$246$	3.70375	0.236142
$247$	−5.28537	−0.336300
$248$	−8.41559	−0.534390
$249$	1.89106	0.119841
$250$	−2.41769	−0.152908
$251$	−9.57536	−0.604391	−0.302196	−	0.953246i	$-0.597720\pi$
$251$	−9.57536	−0.604391	−0.302196	+	0.953246i	$0.597720\pi$
$252$	−0.918421	−0.0578551
$253$	14.7322	0.926208
$254$	48.3065	3.03102
$255$	1.73014	0.108346
$256$	−30.2231	−1.88894
$257$	−0.881268	−0.0549720	−0.0274860	−	0.999622i	$-0.508750\pi$
$257$	−0.881268	−0.0549720	−0.0274860	+	0.999622i	$0.508750\pi$
$258$	−12.9109	−0.803795
$259$	−0.266337	−0.0165494
$260$	6.39386	0.396530
$261$	−7.97153	−0.493425
$262$	−39.8420	−2.46145
$263$	−6.00564	−0.370324	−0.185162	−	0.982708i	$-0.559281\pi$
$263$	−6.00564	−0.370324	−0.185162	+	0.982708i	$0.559281\pi$
$264$	−16.3468	−1.00608
$265$	−11.1272	−0.683539
$266$	0.802712	0.0492174
$267$	13.1575	0.805226
$268$	−52.4117	−3.20155
$269$	15.3180	0.933956	0.466978	−	0.884269i	$-0.345343\pi$
$269$	15.3180	0.933956	0.466978	+	0.884269i	$0.345343\pi$
$270$	−10.7954	−0.656987
$271$	28.8293	1.75125	0.875627	−	0.482987i	$-0.160448\pi$
$271$	28.8293	1.75125	0.875627	+	0.482987i	$0.160448\pi$
$272$	−6.34029	−0.384437
$273$	−0.146701	−0.00887874
$274$	−30.4258	−1.83809
$275$	−4.33837	−0.261614
$276$	11.0287	0.663847
$277$	15.1871	0.912507	0.456253	−	0.889850i	$-0.349191\pi$
$277$	15.1871	0.912507	0.456253	+	0.889850i	$0.349191\pi$
$278$	35.8173	2.14818
$279$	−4.31354	−0.258245
$280$	−0.465986	−0.0278480
$281$	21.8786	1.30517	0.652584	−	0.757716i	$-0.273685\pi$
$281$	21.8786	1.30517	0.652584	+	0.757716i	$0.273685\pi$
$282$	21.8695	1.30231
$283$	−16.0809	−0.955908	−0.477954	−	0.878385i	$-0.658621\pi$
$283$	−16.0809	−0.955908	−0.477954	+	0.878385i	$0.658621\pi$
$284$	−2.00454	−0.118947
$285$	2.68468	0.159027
$286$	17.4410	1.03131
$287$	0.189456	0.0111832
$288$	−3.29055	−0.193897
$289$	−12.8039	−0.753173
$290$	−8.42845	−0.494936
$291$	13.7404	0.805475
$292$	−15.4347	−0.903248
$293$	14.0914	0.823227	0.411613	−	0.911359i	$-0.364965\pi$
$293$	14.0914	0.823227	0.411613	+	0.911359i	$0.364965\pi$
$294$	−14.2719	−0.832353
$295$	13.0910	0.762186
$296$	11.3749	0.661153
$297$	−19.3716	−1.12405
$298$	−28.2789	−1.63815
$299$	−5.64658	−0.326550
$300$	−3.24773	−0.187508
$301$	−0.660423	−0.0380662
$302$	8.06871	0.464302
$303$	6.64766	0.381898
$304$	−9.83829	−0.564265
$305$	−8.38124	−0.479909
$306$	−11.3244	−0.647372
$307$	−17.2957	−0.987117	−0.493559	−	0.869713i	$-0.664304\pi$
$307$	−17.2957	−0.987117	−0.493559	+	0.869713i	$0.664304\pi$
$308$	−1.74251	−0.0992886
$309$	8.64361	0.491718
$310$	−4.56079	−0.259035
$311$	4.52172	0.256403	0.128202	−	0.991748i	$-0.459080\pi$
$311$	4.52172	0.256403	0.128202	+	0.991748i	$0.459080\pi$
$312$	6.26541	0.354709
$313$	29.9128	1.69077	0.845386	−	0.534155i	$-0.179370\pi$
$313$	29.9128	1.69077	0.845386	+	0.534155i	$0.179370\pi$
$314$	8.20803	0.463206
$315$	−0.238848	−0.0134576
$316$	48.0184	2.70125
$317$	10.6496	0.598139	0.299069	−	0.954231i	$-0.403324\pi$
$317$	10.6496	0.598139	0.299069	+	0.954231i	$0.403324\pi$
$318$	−22.7220	−1.27419
$319$	−15.1243	−0.846797
$320$	−9.66955	−0.540544
$321$	−1.29460	−0.0722575
$322$	0.857571	0.0477906
$323$	6.51108	0.362286
$324$	11.8758	0.659769
$325$	1.66281	0.0922363
$326$	−10.6765	−0.591319
$327$	−11.2664	−0.623035
$328$	−8.09142	−0.446774
$329$	1.11868	0.0616748
$330$	−8.85906	−0.487675
$331$	14.3950	0.791219	0.395610	−	0.918419i	$-0.370533\pi$
$331$	14.3950	0.791219	0.395610	+	0.918419i	$0.370533\pi$
$332$	−8.60921	−0.472492
$333$	5.83038	0.319503
$334$	28.3249	1.54987
$335$	−13.6304	−0.744708
$336$	−0.273072	−0.0148973
$337$	−30.9679	−1.68693	−0.843464	−	0.537186i	$-0.819487\pi$
$337$	−30.9679	−1.68693	−0.843464	+	0.537186i	$0.819487\pi$
$338$	24.7451	1.34596
$339$	−11.0578	−0.600579
$340$	−7.87663	−0.427170
$341$	−8.18402	−0.443189
$342$	−17.5722	−0.950194
$343$	−1.46123	−0.0788989
$344$	28.2058	1.52076
$345$	2.86816	0.154416
$346$	25.2838	1.35926
$347$	−12.7815	−0.686146	−0.343073	−	0.939309i	$-0.611468\pi$
$347$	−12.7815	−0.686146	−0.343073	+	0.939309i	$0.611468\pi$
$348$	−11.3221	−0.606930
$349$	4.64674	0.248734	0.124367	−	0.992236i	$-0.460310\pi$
$349$	4.64674	0.248734	0.124367	+	0.992236i	$0.460310\pi$
$350$	−0.252539	−0.0134988
$351$	7.42476	0.396304
$352$	−6.24311	−0.332759
$353$	−4.85486	−0.258398	−0.129199	−	0.991619i	$-0.541241\pi$
$353$	−4.85486	−0.258398	−0.129199	+	0.991619i	$0.541241\pi$
$354$	26.7321	1.42079
$355$	−0.521308	−0.0276681
$356$	−59.9008	−3.17473
$357$	0.180722	0.00956481
$358$	−12.2173	−0.645706
$359$	−29.4161	−1.55252	−0.776262	−	0.630410i	$-0.782887\pi$
$359$	−29.4161	−1.55252	−0.776262	+	0.630410i	$0.782887\pi$
$360$	10.2009	0.537635
$361$	−8.89670	−0.468247
$362$	−29.0751	−1.52815
$363$	−6.60617	−0.346734
$364$	0.667869	0.0350059
$365$	−4.01401	−0.210103
$366$	−17.1147	−0.894600
$367$	−4.40442	−0.229909	−0.114954	−	0.993371i	$-0.536672\pi$
$367$	−4.40442	−0.229909	−0.114954	+	0.993371i	$0.536672\pi$
$368$	−10.5107	−0.547906
$369$	−4.14738	−0.215904
$370$	6.16457	0.320481
$371$	−1.16229	−0.0603431
$372$	−6.12661	−0.317650
$373$	14.9927	0.776294	0.388147	−	0.921597i	$-0.373115\pi$
$373$	14.9927	0.776294	0.388147	+	0.921597i	$0.373115\pi$
$374$	−21.4856	−1.11099
$375$	−0.844619	−0.0436159
$376$	−47.7773	−2.46393
$377$	5.79684	0.298553
$378$	−1.12763	−0.0579991
$379$	6.69151	0.343720	0.171860	−	0.985121i	$-0.445022\pi$
$379$	6.69151	0.343720	0.171860	+	0.985121i	$0.445022\pi$
$380$	−12.2223	−0.626988
$381$	16.8759	0.864579
$382$	−24.7141	−1.26448
$383$	−9.14533	−0.467305	−0.233652	−	0.972320i	$-0.575068\pi$
$383$	−9.14533	−0.467305	−0.233652	+	0.972320i	$0.575068\pi$
$384$	−17.3146	−0.883580
$385$	−0.453164	−0.0230954
$386$	−9.49396	−0.483230
$387$	14.4573	0.734907
$388$	−62.5543	−3.17571
$389$	−0.947406	−0.0480354	−0.0240177	−	0.999712i	$-0.507646\pi$
$389$	−0.947406	−0.0480354	−0.0240177	+	0.999712i	$0.507646\pi$
$390$	3.39551	0.171938
$391$	6.95606	0.351783
$392$	31.1792	1.57479
$393$	−13.9188	−0.702111
$394$	2.02715	0.102126
$395$	12.4879	0.628333
$396$	38.1452	1.91687
$397$	19.6565	0.986530	0.493265	−	0.869879i	$-0.335803\pi$
$397$	19.6565	0.986530	0.493265	+	0.869879i	$0.335803\pi$
$398$	−53.8846	−2.70099
$399$	0.280428	0.0140389
$400$	3.09520	0.154760
$401$	−5.35715	−0.267523	−0.133762	−	0.991014i	$-0.542706\pi$
$401$	−5.35715	−0.267523	−0.133762	+	0.991014i	$0.542706\pi$
$402$	−27.8336	−1.38821
$403$	3.13678	0.156254
$404$	−30.2641	−1.50569
$405$	3.08848	0.153468
$406$	−0.880392	−0.0436931
$407$	11.0619	0.548318
$408$	−7.71839	−0.382117
$409$	1.96328	0.0970781	0.0485390	−	0.998821i	$-0.484543\pi$
$409$	1.96328	0.0970781	0.0485390	+	0.998821i	$0.484543\pi$
$410$	−4.38511	−0.216565
$411$	−10.6292	−0.524302
$412$	−39.3508	−1.93868
$413$	1.36741	0.0672860
$414$	−18.7731	−0.922647
$415$	−2.23895	−0.109906
$416$	2.39286	0.117320
$417$	12.5128	0.612753
$418$	−33.3394	−1.63069
$419$	−19.4882	−0.952062	−0.476031	−	0.879428i	$-0.657925\pi$
$419$	−19.4882	−0.952062	−0.476031	+	0.879428i	$0.657925\pi$
$420$	−0.339241	−0.0165533
$421$	29.4640	1.43599	0.717993	−	0.696050i	$-0.245061\pi$
$421$	29.4640	1.43599	0.717993	+	0.696050i	$0.245061\pi$
$422$	37.1565	1.80875
$423$	−24.4890	−1.19070
$424$	49.6399	2.41073
$425$	−2.04843	−0.0993634
$426$	−1.06452	−0.0515763
$427$	−0.875461	−0.0423665
$428$	5.89379	0.284887
$429$	6.09300	0.294173
$430$	15.2860	0.737157
$431$	29.9583	1.44304	0.721521	−	0.692393i	$-0.243443\pi$
$431$	29.9583	1.44304	0.721521	+	0.692393i	$0.243443\pi$
$432$	13.8206	0.664944
$433$	−33.0683	−1.58916	−0.794581	−	0.607158i	$-0.792309\pi$
$433$	−33.0683	−1.58916	−0.794581	+	0.607158i	$0.792309\pi$
$434$	−0.476396	−0.0228677
$435$	−2.94448	−0.141177
$436$	51.2914	2.45641
$437$	10.7938	0.516337
$438$	−8.19671	−0.391654
$439$	7.52782	0.359283	0.179642	−	0.983732i	$-0.442506\pi$
$439$	7.52782	0.359283	0.179642	+	0.983732i	$0.442506\pi$
$440$	19.3540	0.922667
$441$	15.9814	0.761018
$442$	8.23502	0.391700
$443$	8.00794	0.380469	0.190234	−	0.981739i	$-0.439075\pi$
$443$	8.00794	0.380469	0.190234	+	0.981739i	$0.439075\pi$
$444$	8.28101	0.393000
$445$	−15.5780	−0.738470
$446$	0.275223	0.0130322
$447$	−9.87924	−0.467272
$448$	−1.01003	−0.0477195
$449$	−2.17867	−0.102818	−0.0514088	−	0.998678i	$-0.516371\pi$
$449$	−2.17867	−0.102818	−0.0514088	+	0.998678i	$0.516371\pi$
$450$	5.52833	0.260608
$451$	−7.86877	−0.370526
$452$	50.3418	2.36788
$453$	2.81880	0.132439
$454$	33.2586	1.56090
$455$	0.173689	0.00814266
$456$	−11.9767	−0.560860
$457$	32.2904	1.51048	0.755241	−	0.655447i	$-0.227520\pi$
$457$	32.2904	1.51048	0.755241	+	0.655447i	$0.227520\pi$
$458$	−63.0483	−2.94605
$459$	−9.14661	−0.426927
$460$	−13.0575	−0.608811
$461$	−23.4545	−1.09239	−0.546193	−	0.837659i	$-0.683924\pi$
$461$	−23.4545	−1.09239	−0.546193	+	0.837659i	$0.683924\pi$
$462$	−0.925371	−0.0430522
$463$	−28.8247	−1.33960	−0.669798	−	0.742543i	$-0.733619\pi$
$463$	−28.8247	−1.33960	−0.669798	+	0.742543i	$0.733619\pi$
$464$	10.7904	0.500930
$465$	−1.59331	−0.0738880
$466$	−53.5989	−2.48292
$467$	−1.68316	−0.0778872	−0.0389436	−	0.999241i	$-0.512399\pi$
$467$	−1.68316	−0.0778872	−0.0389436	+	0.999241i	$0.512399\pi$
$468$	−14.6203	−0.675825
$469$	−1.42376	−0.0657431
$470$	−25.8927	−1.19434
$471$	2.86748	0.132126
$472$	−58.4005	−2.68810
$473$	27.4297	1.26122
$474$	25.5005	1.17128
$475$	−3.17857	−0.145843
$476$	−0.822752	−0.0377108
$477$	25.4437	1.16499
$478$	46.8175	2.14138
$479$	−31.2436	−1.42756	−0.713779	−	0.700371i	$-0.753018\pi$
$479$	−31.2436	−1.42756	−0.713779	+	0.700371i	$0.753018\pi$
$480$	−1.21545	−0.0554772
$481$	−4.23981	−0.193319
$482$	12.0336	0.548115
$483$	0.299593	0.0136319
$484$	30.0752	1.36705
$485$	−16.2681	−0.738698
$486$	38.6930	1.75515
$487$	−40.2455	−1.82370	−0.911850	−	0.410524i	$-0.865346\pi$
$487$	−40.2455	−1.82370	−0.911850	+	0.410524i	$0.865346\pi$
$488$	37.3898	1.69256
$489$	−3.72985	−0.168670
$490$	16.8974	0.763348
$491$	−29.1839	−1.31705	−0.658526	−	0.752558i	$-0.728820\pi$
$491$	−29.1839	−1.31705	−0.658526	+	0.752558i	$0.728820\pi$
$492$	−5.89062	−0.265570
$493$	−7.14116	−0.321622
$494$	12.7784	0.574926
$495$	9.92020	0.445880
$496$	5.83886	0.262172
$497$	−0.0544531	−0.00244255
$498$	−4.57198	−0.204875
$499$	−8.91261	−0.398983	−0.199492	−	0.979900i	$-0.563929\pi$
$499$	−8.91261	−0.398983	−0.199492	+	0.979900i	$0.563929\pi$
$500$	3.84521	0.171963
$501$	9.89532	0.442090
$502$	23.1502	1.03324
$503$	13.6653	0.609304	0.304652	−	0.952464i	$-0.401460\pi$
$503$	13.6653	0.609304	0.304652	+	0.952464i	$0.401460\pi$
$504$	1.06553	0.0474626
$505$	−7.87060	−0.350237
$506$	−35.6179	−1.58341
$507$	8.64472	0.383925
$508$	−76.8291	−3.40874
$509$	40.6650	1.80244	0.901222	−	0.433358i	$-0.142671\pi$
$509$	40.6650	1.80244	0.901222	+	0.433358i	$0.142671\pi$
$510$	−4.18294	−0.185224
$511$	−0.419283	−0.0185480
$512$	32.0703	1.41732
$513$	−14.1929	−0.626631
$514$	2.13063	0.0939780
$515$	−10.2337	−0.450952
$516$	20.5340	0.903961
$517$	−46.4627	−2.04343
$518$	0.643919	0.0282922
$519$	8.83290	0.387721
$520$	−7.41803	−0.325302
$521$	13.0700	0.572607	0.286304	−	0.958139i	$-0.407573\pi$
$521$	13.0700	0.572607	0.286304	+	0.958139i	$0.407573\pi$
$522$	19.2727	0.843541
$523$	29.4948	1.28972	0.644859	−	0.764302i	$-0.276916\pi$
$523$	29.4948	1.28972	0.644859	+	0.764302i	$0.276916\pi$
$524$	63.3666	2.76818
$525$	−0.0882245	−0.00385043
$526$	14.5198	0.633091
$527$	−3.86421	−0.168328
$528$	11.3416	0.493581
$529$	−11.4685	−0.498632
$530$	26.9021	1.16855
$531$	−29.9340	−1.29903
$532$	−1.27667	−0.0553508
$533$	3.01595	0.130635
$534$	−31.8107	−1.37658
$535$	1.53276	0.0662671
$536$	60.8070	2.62646
$537$	−4.26813	−0.184183
$538$	−37.0341	−1.59666
$539$	30.3213	1.30603
$540$	17.1695	0.738859
$541$	−5.31616	−0.228560	−0.114280	−	0.993449i	$-0.536456\pi$
$541$	−5.31616	−0.228560	−0.114280	+	0.993449i	$0.536456\pi$
$542$	−69.7002	−2.99388
$543$	−10.1574	−0.435895
$544$	−2.94778	−0.126385
$545$	13.3391	0.571383
$546$	0.354677	0.0151788
$547$	−16.8087	−0.718689	−0.359345	−	0.933205i	$-0.617000\pi$
$547$	−16.8087	−0.718689	−0.359345	+	0.933205i	$0.617000\pi$
$548$	48.3906	2.06714
$549$	19.1647	0.817930
$550$	10.4888	0.447245
$551$	−11.0810	−0.472067
$552$	−12.7952	−0.544601
$553$	1.30442	0.0554695
$554$	−36.7177	−1.55999
$555$	2.15359	0.0914150
$556$	−56.9655	−2.41588
$557$	24.1887	1.02491	0.512455	−	0.858714i	$-0.328736\pi$
$557$	24.1887	1.02491	0.512455	+	0.858714i	$0.328736\pi$
$558$	10.4288	0.441485
$559$	−10.5133	−0.444664
$560$	0.323308	0.0136623
$561$	−7.50600	−0.316904
$562$	−52.8956	−2.23127
$563$	−9.81018	−0.413450	−0.206725	−	0.978399i	$-0.566280\pi$
$563$	−9.81018	−0.413450	−0.206725	+	0.978399i	$0.566280\pi$
$564$	−34.7823	−1.46460
$565$	13.0921	0.550788
$566$	38.8785	1.63418
$567$	0.322606	0.0135482
$568$	2.32562	0.0975809
$569$	28.1377	1.17959	0.589797	−	0.807552i	$-0.299208\pi$
$569$	28.1377	1.17959	0.589797	+	0.807552i	$0.299208\pi$
$570$	−6.49071	−0.271866
$571$	31.0041	1.29748	0.648741	−	0.761009i	$-0.275296\pi$
$571$	31.0041	1.29748	0.648741	+	0.761009i	$0.275296\pi$
$572$	−27.7390	−1.15982
$573$	−8.63387	−0.360685
$574$	−0.458045	−0.0191184
$575$	−3.39580	−0.141615
$576$	22.1106	0.921274
$577$	26.0634	1.08503	0.542516	−	0.840045i	$-0.317472\pi$
$577$	26.0634	1.08503	0.542516	+	0.840045i	$0.317472\pi$
$578$	30.9559	1.28760
$579$	−3.31672	−0.137838
$580$	13.4050	0.556613
$581$	−0.233869	−0.00970250
$582$	−33.2199	−1.37701
$583$	48.2740	1.99930
$584$	17.9070	0.740998
$585$	−3.80222	−0.157202
$586$	−34.0685	−1.40736
$587$	17.6837	0.729886	0.364943	−	0.931030i	$-0.381088\pi$
$587$	17.6837	0.729886	0.364943	+	0.931030i	$0.381088\pi$
$588$	22.6987	0.936079
$589$	−5.99613	−0.247066
$590$	−31.6498	−1.30300
$591$	0.708185	0.0291308
$592$	−7.89207	−0.324362
$593$	24.9555	1.02480	0.512400	−	0.858747i	$-0.328756\pi$
$593$	24.9555	1.02480	0.512400	+	0.858747i	$0.328756\pi$
$594$	46.8345	1.92164
$595$	−0.213968	−0.00877184
$596$	44.9762	1.84230
$597$	−18.8246	−0.770440
$598$	13.6517	0.558258
$599$	3.49052	0.142619	0.0713093	−	0.997454i	$-0.477282\pi$
$599$	3.49052	0.142619	0.0713093	+	0.997454i	$0.477282\pi$
$600$	3.76795	0.153826
$601$	28.5329	1.16388	0.581941	−	0.813231i	$-0.302294\pi$
$601$	28.5329	1.16388	0.581941	+	0.813231i	$0.302294\pi$
$602$	1.59670	0.0650765
$603$	31.1675	1.26924
$604$	−12.8329	−0.522162
$605$	7.82147	0.317988
$606$	−16.0720	−0.652879
$607$	−29.7118	−1.20597	−0.602983	−	0.797754i	$-0.706021\pi$
$607$	−29.7118	−1.20597	−0.602983	+	0.797754i	$0.706021\pi$
$608$	−4.57411	−0.185504
$609$	−0.307565	−0.0124632
$610$	20.2632	0.820433
$611$	17.8082	0.720444
$612$	18.0109	0.728046
$613$	30.9697	1.25085	0.625426	−	0.780283i	$-0.284925\pi$
$613$	30.9697	1.25085	0.625426	+	0.780283i	$0.284925\pi$
$614$	41.8155	1.68754
$615$	−1.53194	−0.0617737
$616$	2.02162	0.0814534
$617$	39.1508	1.57615	0.788077	−	0.615577i	$-0.211077\pi$
$617$	39.1508	1.57615	0.788077	+	0.615577i	$0.211077\pi$
$618$	−20.8975	−0.840622
$619$	1.32237	0.0531507	0.0265754	−	0.999647i	$-0.491540\pi$
$619$	1.32237	0.0531507	0.0265754	+	0.999647i	$0.491540\pi$
$620$	7.25370	0.291315
$621$	−15.1629	−0.608464
$622$	−10.9321	−0.438338
$623$	−1.62720	−0.0651924
$624$	−4.34703	−0.174020
$625$	1.00000	0.0400000
$626$	−72.3198	−2.89048
$627$	−11.6471	−0.465142
$628$	−13.0544	−0.520929
$629$	5.22305	0.208257
$630$	0.577460	0.0230066
$631$	−15.0516	−0.599193	−0.299596	−	0.954066i	$-0.596852\pi$
$631$	−15.0516	−0.599193	−0.299596	+	0.954066i	$0.596852\pi$
$632$	−55.7100	−2.21602
$633$	12.9806	0.515934
$634$	−25.7473	−1.02256
$635$	−19.9805	−0.792901
$636$	36.1382	1.43297
$637$	−11.6216	−0.460463
$638$	36.5658	1.44765
$639$	1.19203	0.0471561
$640$	20.4998	0.810328
$641$	32.6162	1.28826	0.644131	−	0.764915i	$-0.277219\pi$
$641$	32.6162	1.28826	0.644131	+	0.764915i	$0.277219\pi$
$642$	3.12994	0.123529
$643$	24.9480	0.983851	0.491926	−	0.870637i	$-0.336293\pi$
$643$	24.9480	0.983851	0.491926	+	0.870637i	$0.336293\pi$
$644$	−1.36392	−0.0537461
$645$	5.34017	0.210269
$646$	−15.7417	−0.619350
$647$	1.93744	0.0761688	0.0380844	−	0.999275i	$-0.487874\pi$
$647$	1.93744	0.0761688	0.0380844	+	0.999275i	$0.487874\pi$
$648$	−13.7781	−0.541255
$649$	−56.7935	−2.22934
$650$	−4.02016	−0.157684
$651$	−0.166429	−0.00652287
$652$	16.9805	0.665007
$653$	−22.3056	−0.872886	−0.436443	−	0.899732i	$-0.643762\pi$
$653$	−22.3056	−0.872886	−0.436443	+	0.899732i	$0.643762\pi$
$654$	27.2387	1.06512
$655$	16.4794	0.643903
$656$	5.61395	0.219188
$657$	9.17851	0.358088
$658$	−2.70462	−0.105437
$659$	−9.73679	−0.379291	−0.189646	−	0.981853i	$-0.560734\pi$
$659$	−9.73679	−0.379291	−0.189646	+	0.981853i	$0.560734\pi$
$660$	14.0899	0.548448
$661$	−45.3185	−1.76268	−0.881342	−	0.472479i	$-0.843359\pi$
$661$	−45.3185	−1.76268	−0.881342	+	0.472479i	$0.843359\pi$
$662$	−34.8025	−1.35264
$663$	2.87691	0.111730
$664$	9.98822	0.387618
$665$	−0.332017	−0.0128751
$666$	−14.0960	−0.546210
$667$	−11.8383	−0.458382
$668$	−45.0493	−1.74301
$669$	0.0961493	0.00371735
$670$	32.9540	1.27313
$671$	36.3609	1.40370
$672$	−0.126959	−0.00489755
$673$	24.7710	0.954851	0.477425	−	0.878672i	$-0.341570\pi$
$673$	24.7710	0.954851	0.477425	+	0.878672i	$0.341570\pi$
$674$	74.8706	2.88391
$675$	4.46518	0.171865
$676$	−39.3559	−1.51369
$677$	−20.6154	−0.792314	−0.396157	−	0.918183i	$-0.629656\pi$
$677$	−20.6154	−0.792314	−0.396157	+	0.918183i	$0.629656\pi$
$678$	26.7344	1.02673
$679$	−1.69928	−0.0652125
$680$	9.13831	0.350438
$681$	11.6189	0.445237
$682$	19.7864	0.757660
$683$	0.616035	0.0235719	0.0117860	−	0.999931i	$-0.496248\pi$
$683$	0.616035	0.0235719	0.0117860	+	0.999931i	$0.496248\pi$
$684$	27.9476	1.06860
$685$	12.5847	0.480835
$686$	3.53279	0.134882
$687$	−22.0259	−0.840342
$688$	−19.5696	−0.746084
$689$	−18.5025	−0.704888
$690$	−6.93430	−0.263984
$691$	17.8270	0.678173	0.339086	−	0.940755i	$-0.389882\pi$
$691$	17.8270	0.678173	0.339086	+	0.940755i	$0.389882\pi$
$692$	−40.2126	−1.52865
$693$	1.03621	0.0393625
$694$	30.9016	1.17301
$695$	−14.8147	−0.561953
$696$	13.1357	0.497908
$697$	−3.71536	−0.140729
$698$	−11.2343	−0.425226
$699$	−18.7248	−0.708236
$700$	0.401650	0.0151809
$701$	18.7168	0.706922	0.353461	−	0.935449i	$-0.385005\pi$
$701$	18.7168	0.706922	0.353461	+	0.935449i	$0.385005\pi$
$702$	−17.9507	−0.677507
$703$	8.10466	0.305673
$704$	41.9501	1.58105
$705$	−9.04562	−0.340678
$706$	11.7375	0.441748
$707$	−0.822122	−0.0309191
$708$	−42.5160	−1.59785
$709$	22.1260	0.830961	0.415481	−	0.909602i	$-0.363613\pi$
$709$	22.1260	0.830961	0.415481	+	0.909602i	$0.363613\pi$
$710$	1.26036	0.0473004
$711$	−28.5550	−1.07090
$712$	69.4956	2.60446
$713$	−6.40592	−0.239904
$714$	−0.436928	−0.0163516
$715$	−7.21391	−0.269785
$716$	19.4310	0.726172
$717$	16.3557	0.610815
$718$	71.1190	2.65414
$719$	23.8375	0.888987	0.444493	−	0.895782i	$-0.353384\pi$
$719$	23.8375	0.888987	0.444493	+	0.895782i	$0.353384\pi$
$720$	−7.07753	−0.263764
$721$	−1.06896	−0.0398102
$722$	21.5094	0.800498
$723$	4.20394	0.156346
$724$	46.2424	1.71859
$725$	3.48617	0.129473
$726$	15.9716	0.592763
$727$	35.9199	1.33220	0.666098	−	0.745864i	$-0.267963\pi$
$727$	35.9199	1.33220	0.666098	+	0.745864i	$0.267963\pi$
$728$	−0.774848	−0.0287178
$729$	4.25195	0.157480
$730$	9.70462	0.359184
$731$	12.9514	0.479023
$732$	27.2200	1.00608
$733$	49.6436	1.83363	0.916813	−	0.399316i	$-0.130752\pi$
$733$	49.6436	1.83363	0.916813	+	0.399316i	$0.130752\pi$
$734$	10.6485	0.393043
$735$	5.90312	0.217740
$736$	−4.88671	−0.180127
$737$	59.1337	2.17822
$738$	10.0271	0.369101
$739$	−5.97744	−0.219884	−0.109942	−	0.993938i	$-0.535066\pi$
$739$	−5.97744	−0.219884	−0.109942	+	0.993938i	$0.535066\pi$
$740$	−9.80444	−0.360418
$741$	4.46412	0.163994
$742$	2.81005	0.103160
$743$	−17.2264	−0.631977	−0.315988	−	0.948763i	$-0.602336\pi$
$743$	−17.2264	−0.631977	−0.315988	+	0.948763i	$0.602336\pi$
$744$	7.10797	0.260591
$745$	11.6967	0.428533
$746$	−36.2477	−1.32712
$747$	5.11962	0.187317
$748$	34.1718	1.24944
$749$	0.160104	0.00585008
$750$	2.04202	0.0745642
$751$	46.3306	1.69063	0.845313	−	0.534272i	$-0.179414\pi$
$751$	46.3306	1.69063	0.845313	+	0.534272i	$0.179414\pi$
$752$	33.1486	1.20881
$753$	8.08753	0.294726
$754$	−14.0149	−0.510394
$755$	−3.33737	−0.121459
$756$	1.79344	0.0652268
$757$	−35.9850	−1.30790	−0.653949	−	0.756538i	$-0.726889\pi$
$757$	−35.9850	−1.30790	−0.653949	+	0.756538i	$0.726889\pi$
$758$	−16.1780	−0.587611
$759$	−12.4431	−0.451657
$760$	14.1800	0.514363
$761$	50.2019	1.81982	0.909908	−	0.414810i	$-0.136152\pi$
$761$	50.2019	1.81982	0.909908	+	0.414810i	$0.136152\pi$
$762$	−40.8006	−1.47805
$763$	1.39333	0.0504419
$764$	39.3065	1.42206
$765$	4.68398	0.169350
$766$	22.1105	0.798886
$767$	21.7678	0.785991
$768$	25.5270	0.921126
$769$	34.4616	1.24272	0.621358	−	0.783527i	$-0.286581\pi$
$769$	34.4616	1.24272	0.621358	+	0.783527i	$0.286581\pi$
$770$	1.09561	0.0394830
$771$	0.744336	0.0268066
$772$	15.0997	0.543449
$773$	34.1443	1.22808	0.614042	−	0.789274i	$-0.289543\pi$
$773$	34.1443	1.22808	0.614042	+	0.789274i	$0.289543\pi$
$774$	−34.9533	−1.25637
$775$	1.88643	0.0677624
$776$	72.5742	2.60526
$777$	0.224953	0.00807015
$778$	2.29053	0.0821195
$779$	−5.76517	−0.206559
$780$	−5.40038	−0.193365
$781$	2.26163	0.0809274
$782$	−16.8176	−0.601395
$783$	15.5664	0.556296
$784$	−21.6326	−0.772593
$785$	−3.39499	−0.121173
$786$	33.6513	1.20030
$787$	49.1699	1.75272	0.876359	−	0.481659i	$-0.159965\pi$
$787$	49.1699	1.75272	0.876359	+	0.481659i	$0.159965\pi$
$788$	−3.22407	−0.114853
$789$	5.07248	0.180585
$790$	−30.1917	−1.07417
$791$	1.36753	0.0486238
$792$	−44.2553	−1.57254
$793$	−13.9364	−0.494898
$794$	−47.5232	−1.68654
$795$	9.39825	0.333322
$796$	85.7007	3.03758
$797$	−1.19443	−0.0423089	−0.0211544	−	0.999776i	$-0.506734\pi$
$797$	−1.19443	−0.0423089	−0.0211544	+	0.999776i	$0.506734\pi$
$798$	−0.677986	−0.0240004
$799$	−21.9381	−0.776113
$800$	1.43905	0.0508779
$801$	35.6210	1.25861
$802$	12.9519	0.457348
$803$	17.4143	0.614537
$804$	44.2679	1.56121
$805$	−0.354707	−0.0125018
$806$	−7.58374	−0.267126
$807$	−12.9379	−0.455435
$808$	35.1118	1.23523
$809$	26.1186	0.918281	0.459141	−	0.888364i	$-0.348157\pi$
$809$	26.1186	0.918281	0.459141	+	0.888364i	$0.348157\pi$
$810$	−7.46697	−0.262363
$811$	21.4096	0.751794	0.375897	−	0.926661i	$-0.377335\pi$
$811$	21.4096	0.751794	0.375897	+	0.926661i	$0.377335\pi$
$812$	1.40022	0.0491380
$813$	−24.3498	−0.853984
$814$	−26.7442	−0.937384
$815$	4.41601	0.154686
$816$	5.35513	0.187467
$817$	20.0967	0.703096
$818$	−4.74660	−0.165961
$819$	−0.397160	−0.0138779
$820$	6.97429	0.243553
$821$	−40.4726	−1.41250	−0.706252	−	0.707960i	$-0.749616\pi$
$821$	−40.4726	−1.41250	−0.706252	+	0.707960i	$0.749616\pi$
$822$	25.6982	0.896327
$823$	−26.8616	−0.936335	−0.468168	−	0.883640i	$-0.655086\pi$
$823$	−26.8616	−0.936335	−0.468168	+	0.883640i	$0.655086\pi$
$824$	45.6540	1.59043
$825$	3.66427	0.127574
$826$	−3.30598	−0.115030
$827$	−9.44610	−0.328473	−0.164237	−	0.986421i	$-0.552516\pi$
$827$	−9.44610	−0.328473	−0.164237	+	0.986421i	$0.552516\pi$
$828$	29.8576	1.03762
$829$	53.9909	1.87518	0.937590	−	0.347743i	$-0.113052\pi$
$829$	53.9909	1.87518	0.937590	+	0.347743i	$0.113052\pi$
$830$	5.41307	0.187890
$831$	−12.8274	−0.444976
$832$	−16.0787	−0.557427
$833$	14.3167	0.496043
$834$	−30.2520	−1.04754
$835$	−11.7157	−0.405439
$836$	53.0247	1.83390
$837$	8.42323	0.291149
$838$	47.1164	1.62761
$839$	0.817512	0.0282237	0.0141118	−	0.999900i	$-0.495508\pi$
$839$	0.817512	0.0282237	0.0141118	+	0.999900i	$0.495508\pi$
$840$	0.393581	0.0135798
$841$	−16.8467	−0.580919
$842$	−71.2347	−2.45491
$843$	−18.4791	−0.636454
$844$	−59.0955	−2.03415
$845$	−10.2350	−0.352096
$846$	59.2067	2.03557
$847$	0.816990	0.0280721
$848$	−34.4409	−1.18270
$849$	13.5822	0.466140
$850$	4.95246	0.169868
$851$	8.65855	0.296811
$852$	1.69307	0.0580036
$853$	−3.25549	−0.111466	−0.0557330	−	0.998446i	$-0.517750\pi$
$853$	−3.25549	−0.111466	−0.0557330	+	0.998446i	$0.517750\pi$
$854$	2.11659	0.0724282
$855$	7.26817	0.248566
$856$	−6.83785	−0.233713
$857$	−6.87376	−0.234803	−0.117402	−	0.993085i	$-0.537456\pi$
$857$	−6.87376	−0.234803	−0.117402	+	0.993085i	$0.537456\pi$
$858$	−14.7310	−0.502907
$859$	0.0404079	0.00137870	0.000689349	−	1.00000i	$-0.499781\pi$
$859$	0.0404079	0.00137870	0.000689349		1.00000i	$0.499781\pi$
$860$	−24.3116	−0.829019
$861$	−0.160018	−0.00545341
$862$	−72.4298	−2.46697
$863$	−6.31529	−0.214975	−0.107487	−	0.994206i	$-0.534281\pi$
$863$	−6.31529	−0.214975	−0.107487	+	0.994206i	$0.534281\pi$
$864$	6.42560	0.218603
$865$	−10.4578	−0.355577
$866$	79.9488	2.71677
$867$	10.8144	0.367278
$868$	0.757683	0.0257174
$869$	−54.1770	−1.83783
$870$	7.11883	0.241351
$871$	−22.6648	−0.767968
$872$	−59.5073	−2.01517
$873$	37.1990	1.25900
$874$	−26.0960	−0.882710
$875$	0.104455	0.00353122
$876$	13.0364	0.440461
$877$	−48.9066	−1.65146	−0.825730	−	0.564066i	$-0.809236\pi$
$877$	−48.9066	−1.65146	−0.825730	+	0.564066i	$0.809236\pi$
$878$	−18.1999	−0.614217
$879$	−11.9018	−0.401439
$880$	−13.4281	−0.452661
$881$	−19.0695	−0.642469	−0.321235	−	0.947000i	$-0.604098\pi$
$881$	−19.0695	−0.642469	−0.321235	+	0.947000i	$0.604098\pi$
$882$	−38.6380	−1.30101
$883$	35.3490	1.18959	0.594794	−	0.803878i	$-0.297234\pi$
$883$	35.3490	1.18959	0.594794	+	0.803878i	$0.297234\pi$
$884$	−13.0974	−0.440512
$885$	−11.0569	−0.371673
$886$	−19.3607	−0.650435
$887$	34.5067	1.15862	0.579311	−	0.815107i	$-0.303322\pi$
$887$	34.5067	1.15862	0.579311	+	0.815107i	$0.303322\pi$
$888$	−9.60746	−0.322405
$889$	−2.08706	−0.0699976
$890$	37.6628	1.26246
$891$	−13.3990	−0.448883
$892$	−0.437729	−0.0146562
$893$	−34.0415	−1.13916
$894$	23.8849	0.798831
$895$	5.05332	0.168914
$896$	2.14131	0.0715360
$897$	4.76921	0.159239
$898$	5.26733	0.175773
$899$	6.57639	0.219335
$900$	−8.79252	−0.293084
$901$	22.7933	0.759355
$902$	19.0242	0.633437
$903$	0.557806	0.0185626
$904$	−58.4055	−1.94254
$905$	12.0260	0.399757
$906$	−6.81498	−0.226413
$907$	12.5195	0.415703	0.207851	−	0.978160i	$-0.433353\pi$
$907$	12.5195	0.415703	0.207851	+	0.978160i	$0.433353\pi$
$908$	−52.8961	−1.75542
$909$	17.9971	0.596925
$910$	−0.419925	−0.0139204
$911$	−14.5086	−0.480692	−0.240346	−	0.970687i	$-0.577261\pi$
$911$	−14.5086	−0.480692	−0.240346	+	0.970687i	$0.577261\pi$
$912$	8.30961	0.275159
$913$	9.71338	0.321466
$914$	−78.0681	−2.58226
$915$	7.07896	0.234023
$916$	100.275	3.31318
$917$	1.72135	0.0568440
$918$	22.1136	0.729858
$919$	43.6588	1.44017	0.720085	−	0.693885i	$-0.244103\pi$
$919$	43.6588	1.44017	0.720085	+	0.693885i	$0.244103\pi$
$920$	15.1491	0.499451
$921$	14.6083	0.481359
$922$	56.7057	1.86750
$923$	−0.866838	−0.0285323
$924$	1.47176	0.0484172
$925$	−2.54978	−0.0838363
$926$	69.6890	2.29012
$927$	23.4007	0.768578
$928$	5.01675	0.164683
$929$	37.3685	1.22602	0.613010	−	0.790075i	$-0.289958\pi$
$929$	37.3685	1.22602	0.613010	+	0.790075i	$0.289958\pi$
$930$	3.85213	0.126316
$931$	22.2153	0.728077
$932$	85.2462	2.79233
$933$	−3.81913	−0.125033
$934$	4.06935	0.133153
$935$	8.88685	0.290631
$936$	16.9622	0.554427
$937$	−6.91459	−0.225890	−0.112945	−	0.993601i	$-0.536028\pi$
$937$	−6.91459	−0.225890	−0.112945	+	0.993601i	$0.536028\pi$
$938$	3.44221	0.112392
$939$	−25.2649	−0.824490
$940$	41.1810	1.34318
$941$	−11.8124	−0.385074	−0.192537	−	0.981290i	$-0.561672\pi$
$941$	−11.8124	−0.385074	−0.192537	+	0.981290i	$0.561672\pi$
$942$	−6.93266	−0.225878
$943$	−6.15917	−0.200570
$944$	40.5191	1.31878
$945$	0.466409	0.0151723
$946$	−66.3164	−2.15613
$947$	−58.2529	−1.89297	−0.946483	−	0.322754i	$-0.895391\pi$
$947$	−58.2529	−1.89297	−0.946483	+	0.322754i	$0.895391\pi$
$948$	−40.5573	−1.31724
$949$	−6.67456	−0.216665
$950$	7.68478	0.249327
$951$	−8.99482	−0.291677
$952$	0.954540	0.0309368
$953$	−4.74730	−0.153780	−0.0768900	−	0.997040i	$-0.524499\pi$
$953$	−4.74730	−0.153780	−0.0768900	+	0.997040i	$0.524499\pi$
$954$	−61.5148	−1.99162
$955$	10.2222	0.330783
$956$	−74.4608	−2.40824
$957$	12.7743	0.412933
$958$	75.5373	2.44050
$959$	1.31453	0.0424483
$960$	8.16709	0.263592
$961$	−27.4414	−0.885206
$962$	10.2505	0.330491
$963$	−3.50484	−0.112942
$964$	−19.1388	−0.616420
$965$	3.92688	0.126411
$966$	−0.724321	−0.0233047
$967$	6.34545	0.204056	0.102028	−	0.994782i	$-0.467467\pi$
$967$	6.34545	0.204056	0.102028	+	0.994782i	$0.467467\pi$
$968$	−34.8926	−1.12149
$969$	−5.49938	−0.176666
$970$	39.3312	1.26285
$971$	49.5490	1.59010	0.795051	−	0.606542i	$-0.207444\pi$
$971$	49.5490	1.59010	0.795051	+	0.606542i	$0.207444\pi$
$972$	−61.5392	−1.97387
$973$	−1.54747	−0.0496095
$974$	97.3011	3.11773
$975$	−1.40444	−0.0449782
$976$	−25.9416	−0.830370
$977$	−33.9307	−1.08554	−0.542770	−	0.839881i	$-0.682625\pi$
$977$	−33.9307	−1.08554	−0.542770	+	0.839881i	$0.682625\pi$
$978$	9.01761	0.288351
$979$	67.5833	2.15997
$980$	−26.8745	−0.858474
$981$	−30.5013	−0.973833
$982$	70.5576	2.25158
$983$	−52.2834	−1.66758	−0.833791	−	0.552080i	$-0.813834\pi$
$983$	−52.2834	−1.66758	−0.833791	+	0.552080i	$0.813834\pi$
$984$	6.83417	0.217865
$985$	−0.838466	−0.0267158
$986$	17.2651	0.549833
$987$	−0.944858	−0.0300752
$988$	−20.3233	−0.646571
$989$	21.4702	0.682713
$990$	−23.9839	−0.762259
$991$	−48.3161	−1.53481	−0.767406	−	0.641162i	$-0.778453\pi$
$991$	−48.3161	−1.53481	−0.767406	+	0.641162i	$0.778453\pi$
$992$	2.71465	0.0861903
$993$	−12.1583	−0.385831
$994$	0.131650	0.00417570
$995$	22.2877	0.706567
$996$	7.27150	0.230406
$997$	−39.3971	−1.24772	−0.623860	−	0.781536i	$-0.714436\pi$
$997$	−39.3971	−1.24772	−0.623860	+	0.781536i	$0.714436\pi$
$998$	21.5479	0.682087
$999$	−11.3852	−0.360213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.14	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.14	✓	153	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41769 q^{2} -0.844619 q^{3} +3.84521 q^{4} +1.00000 q^{5} +2.04202 q^{6} +0.104455 q^{7} -4.46113 q^{8} -2.28662 q^{9} +O(q^{10})\)	\(q-2.41769 q^{2} -0.844619 q^{3} +3.84521 q^{4} +1.00000 q^{5} +2.04202 q^{6} +0.104455 q^{7} -4.46113 q^{8} -2.28662 q^{9} -2.41769 q^{10} -4.33837 q^{11} -3.24773 q^{12} +1.66281 q^{13} -0.252539 q^{14} -0.844619 q^{15} +3.09520 q^{16} -2.04843 q^{17} +5.52833 q^{18} -3.17857 q^{19} +3.84521 q^{20} -0.0882245 q^{21} +10.4888 q^{22} -3.39580 q^{23} +3.76795 q^{24} +1.00000 q^{25} -4.02016 q^{26} +4.46518 q^{27} +0.401650 q^{28} +3.48617 q^{29} +2.04202 q^{30} +1.88643 q^{31} +1.43905 q^{32} +3.66427 q^{33} +4.95246 q^{34} +0.104455 q^{35} -8.79252 q^{36} -2.54978 q^{37} +7.68478 q^{38} -1.40444 q^{39} -4.46113 q^{40} +1.81376 q^{41} +0.213299 q^{42} -6.32258 q^{43} -16.6819 q^{44} -2.28662 q^{45} +8.20998 q^{46} +10.7097 q^{47} -2.61426 q^{48} -6.98909 q^{49} -2.41769 q^{50} +1.73014 q^{51} +6.39386 q^{52} -11.1272 q^{53} -10.7954 q^{54} -4.33837 q^{55} -0.465986 q^{56} +2.68468 q^{57} -8.42845 q^{58} +13.0910 q^{59} -3.24773 q^{60} -8.38124 q^{61} -4.56079 q^{62} -0.238848 q^{63} -9.66955 q^{64} +1.66281 q^{65} -8.85906 q^{66} -13.6304 q^{67} -7.87663 q^{68} +2.86816 q^{69} -0.252539 q^{70} -0.521308 q^{71} +10.2009 q^{72} -4.01401 q^{73} +6.16457 q^{74} -0.844619 q^{75} -12.2223 q^{76} -0.453164 q^{77} +3.39551 q^{78} +12.4879 q^{79} +3.09520 q^{80} +3.08848 q^{81} -4.38511 q^{82} -2.23895 q^{83} -0.339241 q^{84} -2.04843 q^{85} +15.2860 q^{86} -2.94448 q^{87} +19.3540 q^{88} -15.5780 q^{89} +5.52833 q^{90} +0.173689 q^{91} -13.0575 q^{92} -1.59331 q^{93} -25.8927 q^{94} -3.17857 q^{95} -1.21545 q^{96} -16.2681 q^{97} +16.8974 q^{98} +9.92020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

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